To solve the expression \( 25x^2 - 81 \), you can factor it using the difference of squares method.

### Step 1: Recognize the difference of squares.
The expression is of the form \( a^2 - b^2 \), where:

- \( a = 5x \) (since \( (5x)^2 = 25x^2 \))
- \( b = 9 \) (since \( 9^2 = 81 \))

### Step 2: Apply the difference of squares formula.
The difference of squares formula is:

\[
a^2 - b^2 = (a - b)(a + b)
\]

### Step 3: Substitute the values of \( a \) and \( b \) into the formula.

\[
25x^2 - 81 = (5x - 9)(5x + 9)
\]

So, the expression \( 25x^2 - 81 \) factors to:

\[
(5x - 9)(5x + 9)
\]

Would you like more details or have any questions?

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Here are five related questions:

1. How do you solve a quadratic equation like \( (5x - 9)(5x + 9) = 0 \)?
2. Can you explain how to factor expressions that are not perfect squares?
3. What are some real-life applications of the difference of squares formula?
4. How would you expand \( (5x - 9)(5x + 9) \) back to the original expression?
5. How does factoring help in solving polynomial equations?

**Tip:** Remember, recognizing patterns like the difference of squares can simplify the process of factoring complex expressions!

Learn how to factor the expression 25x^2 - 81 using the difference of squares method. This problem demonstrates the application of algebraic concepts and the difference of squares formula. Suitable for Grades 9-12 students.

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